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# Solved: (a) Assuming the dimensions of the nucleus and ISBN: 9780321809247 1

## Solution for problem 91 Chapter 2

Chemistry: A Molecular Approach | 3rd Edition

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Problem 91

(a) Assuming the dimensions of the nucleus and atom shown in Figure 2.10, what fraction of the volume of the atom is taken up by the nucleus? -15? b) Using the mass of the proton from Table and assuming its diameter is 1.0 × 10? m, calculate the density of a proton in g/cm3.

Step-by-Step Solution:

Solution Step 1 : (a) Assuming the dimensions of the nucleus and atom shown in Figure 2.10, what fraction of the volume of the atom is taken up by the nucleus Atom is made up of subatomic particles which are protons, neutrons and electrons. Protons and neutrons make the nucleus of atom and the the nucleus is located at the centre of the atom and takes most of the mass of the atom. From the figure, given in the question, we get the diameter of atom and nucleus. Therefore, Diameter of atom = 1 - 5 10 -10m [1 = 1 × 10 -1m] -15 Diameter of nucleus 10 m We calculate the volume of the atom using the formula to find volume of sphere as both atom and nucleus are spherical in shape. Formula to find volume of sphere is : 4 3 V = 3r where, v = volume, r = radius and = 22/7 or 3.1415 radius(r) is twice the diameter(d). Therefore, Step 2: Now, we substitute the values in the formula to calculate volume of atom : -30 3 V = 0.407 × 10 m . Similarly we calculate the volume of nucleus : V = 0.407 × 10 -4m . Now we calculate the percentage of the volume of atom taken by nucleus is : -30 3 From above calculations, we got the volume of atom as 0.407 × 10 m and volume -45 3 of nucleus as 0.407 × 10 m . Therefore, percentage = -15 = 100 × 10 % = 10 13% Step 3 : b) Using the mass of the proton from Table and assuming its diameter is 1.0 × 10 -15m, calculate the density of a proton in g/cm3. Formula to calculate density of a particle : where, = density V = volume m = mass We calculate volume of proton using volume of sphere formula as proton is spherical in shape : 4 3 V = 3r where, v = volume, r = radius and = 22/7 or 3.1415 We know mass of proton = 1.0073 amu. Given, diameter of proton = 1.0 × 10 -15m. Radius is twice the diameter. Hence radius of proton is : -15 = 0.5 × 10 m. To convert in cm : = 0.5 × 10 cm.

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##### ISBN: 9780321809247

Chemistry: A Molecular Approach was written by and is associated to the ISBN: 9780321809247. The answer to “(a) Assuming the dimensions of the nucleus and atom shown in Figure 2.10, what fraction of the volume of the atom is taken up by the nucleus? -15? b) Using the mass of the proton from Table and assuming its diameter is 1.0 × 10? m, calculate the density of a proton in g/cm3.” is broken down into a number of easy to follow steps, and 54 words. The full step-by-step solution to problem: 91 from chapter: 2 was answered by , our top Chemistry solution expert on 02/22/17, 04:35PM. This textbook survival guide was created for the textbook: Chemistry: A Molecular Approach, edition: 3. This full solution covers the following key subjects: assuming, atom, proton, nucleus, its. This expansive textbook survival guide covers 82 chapters, and 9454 solutions. Since the solution to 91 from 2 chapter was answered, more than 367 students have viewed the full step-by-step answer.

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